Real-time compensation of high-order concomitant magnetic fields

ABSTRACT

A method, electromagnet device, and system for reducing a higher order term of a concomitant field in an imaging magnetic field during magnetic resonance imaging is described. The electromagnet system has a first shim coil configured to be driven to generate a first compensation magnetic field during imaging according to a first second-order compensation term, the first compensation magnetic field having a similar amplitude but opposite direction as that of a first second-order concomitant magnetic field.

CROSS-REFERENCE TO RELATED APPLICATION

This application is a continuation of U.S. patent application Ser. No.16/590,979 filed Oct. 2, 2019, titled REAL-TIME COMPENSATION OFHIGH-ORDER CONCOMITANT MAGNETIC FIELDS, the contents of which are herebyexpressly incorporated into the present application by reference intheir entirety.

FIELD

The present disclosure is related to systems and methods for magneticresonance. More particularly, the disclosure relates to systems andmethods for concomitant field correction and compensation.

BACKGROUND

Magnetic resonance imaging (MRI) is generally performed with very strongstatic magnetic fields. The static magnetic field, also referred to asthe “main field” or “B0 field”, is responsible for polarizing nuclei andis required for imaging during nuclear magnetic resonance.

Due to Maxwell's equations, whenever a linear gradient field isproduced, e.g. for spatial encoding, it is accompanied by secondary orsecond-order field terms, typically known as second order concomitantmagnetic fields or just concomitant fields. Depending on the gradientcoil design, the zeroth and first order terms can be eliminated.However, the higher-order distortion terms (i.e., 2nd order and above)are usually unavoidable.

The higher-order concomitant magnetic fields can lead to phase errors,signal dropout, and/or imaging artefacts that are undesirable. Theseproblems become of greater importance as the gradient strength of animaging sequence is increased and/or the main magnetic field strength ofan MR system is decreased.

Thus, there remains a need to provide systems and methods for reducingor otherwise eliminating higher-order concomitant magnetic field inmagnetic resonance systems.

SUMMARY

In some examples, the present disclosure provides a magnetic resonanceimaging (MRI) system comprising: an electromagnet system for reducing ahigher order term of a concomitant field in an imaging magnetic fieldduring magnetic resonance imaging, the electromagnet system having: afirst shim coil configured to be driven to generate a first compensationmagnetic field during imaging according to a first second-ordercompensation term, the first compensation magnetic field having asimilar amplitude but opposite direction as that of a first second-orderconcomitant magnetic field.

In some examples, the present disclosure provides a method for reducinga higher order term of a concomitant field in an imaging magnetic fieldduring magnetic resonance imaging, the method comprising: generating afirst compensation magnetic field with a first shim coil during imagingaccording to a first second-order compensation term, the firstcompensation magnetic field having a similar amplitude but oppositedirection as that of a first second-order concomitant magnetic field.

In some examples, the present disclosure provides an electromagnet forreducing a higher order term of a concomitant field in an imagingmagnetic field during magnetic resonance imaging, the electromagnetconfigured to be driven to generate a first compensation magnetic fieldduring imaging according to a first second-order compensation term, thefirst compensation magnetic field having a similar amplitude butopposite direction as that of a first second-order concomitant magneticfield.

The foregoing and other aspects and advantages of the present disclosurewill appear from the following description. In the description,reference is made to the accompanying drawings that form a part hereof,and in which there is shown by way of illustration a preferredembodiment. Such embodiment does not necessarily represent the fullscope of the disclosure, however, and reference is made therefore to theclaims and herein for interpreting the scope of the disclosure.

BRIEF DESCRIPTION OF THE DRAWINGS

Reference will now be made, by way of example, to the accompanyingdrawings which show example embodiments of the present application, andin which:

FIG. 1 is a block diagram of a magnetic resonance imaging (MRI) systemin accordance with an example embodiment of the present disclosure;

FIG. 2 is a schematic of an electromagnet according to an exampleembodiment of the present disclosure for reducing a higher order term ofa concomitant field in an imaging magnetic field during magneticresonance imaging;

FIG. 3 illustrates the z-component of the magnetic field in the xz-planethat the wire pattern shown in FIG. 2 produces;

FIG. 4 illustrates the z-component of the magnetic field in the xy-planethat the wire pattern shown in FIG. 2 produces;

FIG. 5 is a flowchart setting forth the steps of an example method forreducing a higher order term of a concomitant field in an imagingmagnetic field during magnetic resonance imaging;

FIG. 6 is a flowchart setting forth the steps of another example methodfor reducing a higher order term of a concomitant field in an imagingmagnetic field during magnetic resonance imaging; and

FIG. 7 shows an example of signal dropout caused by concomitant magneticfields.

DETAILED DESCRIPTION

Described herein are systems, devices, and methods for reducing higherorder terms (i.e., 2nd order or higher) of a concomitant field in animaging magnetic field during magnetic resonance imaging.Inhomogeneities present in the imaging magnetic field of a magneticresonance imaging system are often mitigated or removed via a shimmingprocess.

Referring to FIG. 1, a block diagram of an example magnetic resonanceimaging (MRI) system is shown at 100 in accordance with an exampleembodiment. The example implementation of MRI system indicated at 100 isfor illustrative purposes only, and variations including additional,fewer and/or varied components are possible.

As shown in FIG. 1, the illustrative MRI system 100 comprises a dataprocessing system 102. The data processing system 102 can generallyinclude one or more output devices such as a display, one or more inputdevices such as a keyboard and a mouse as well as one or more processorsconnected to a memory having volatile and persistent components. Thedata processing system 102 may further comprise one or more interfacesadapted for communication and data exchange with the hardware componentsof MRI system 100 used for performing a scan. As shown, data processingsystem 102 includes a memory 104 and a processor 106 for controlling thecommunication and data exchange with the hardware components.

Continuing with FIG. 1, example MRI system 100 also includes a mainfield magnet 110. The main field magnet 110 may be implemented as apermanent, superconducting or a resistive magnet, for example. Othermagnet types, including hybrid magnets suitable for use in MRI system100 are contemplated. Main field magnet 110 is operable to produce asubstantially uniform main magnetic field having strength B0 and adirection along an axis. The main magnetic field is used to create animaging volume therein within which desired atomic nuclei, such as theprotons in hydrogen within water and fat, of an object are magneticallyaligned in preparation for a scan. In some implementations, as in thisexample implementation, a main field control unit 115 in communicationwith data processing system 105 may be used for controlling theoperation of main field magnet 110.

The MRI system 100 further includes radio frequency (RF) coils 120. TheRF coils 120 are used to establish an RF magnetic field with strength B1to excite the atomic nuclei or “spins”. The RF coils 120 can also detectsignals emitted from the “relaxing” spins within the object beingimaged. Accordingly, the RF coils 120 may be in the form of separatetransmit and receive coils or a combined transmit and receive coil witha switching mechanism for switching between transmit and receive modes.

The RF coils 120 may be implemented as surface coils, which aretypically receive only coils and/or volume coils which can be receiveand transmit coils. RF coils 120 can be integrated in the main fieldmagnet 110 bore. Alternatively, RF coils 120 may be implemented incloser proximity to the object to be scanned, such as a head, and cantake a shape that approximates the shape of the object, such as aclose-fitting helmet. An RF coil control unit 125 in communication withdata processing system 102 may be used to control the operation of theRF coils 120 in either a transmit aspect or a receive aspect.

To obtain images from the MRI system 100, one or more sets of RF pulsesand gradient waveforms (collectively called “pulse sequences”) areselected at the data processing system 102. The data processing system102 communicates the selected pulse sequence information to the RFcontrol unit 125 and one or more gradient coil systems, discussed inmore detail below, which collectively generate the associated waveformsand timings for providing a sequence of pulses to perform a scan.

The gradient coil system includes gradient coils 130, which producecontrolled and uniform linear gradients with the main magnetic field.For example, gradient coils 130 may include three orthogonalcurrent-carrying gradient coils, the x gradient coil, the y gradientcoil, and the z gradient coil. When there are three orthogonal gradientaxes, each gradient coil 130 may be configured to generate a magneticfield that varies linearly along one of the three gradient axes. Alongwith the main field magnet 110, gradient coils 130 may be designed toproduce a desired linear-gradient magnetic field along each x, y, and zaxis. Each gradient coil 130 may be used individually or in combinationwith one another.

In addition to allowing spatial excitation, gradient coils 130 mayattach spatially specific frequency and phase information to the atomicnuclei placed within the imaging volume, allowing the resultant MRsignal to be reconstructed into a useful image. A gradient coil controlunit 135, in communication with data processing system 102, is used tocontrol the operation of gradient coils 130. Generally, the imagingvolume may be defined as the region in which MR images of interest areobtained using the MRI apparatus. The imaging volume may be a sphericalvolume that is smaller than the total volume of space within gradientcoils 130.

In the present embodiment, MRI system 100 further includes shim coils 10and a shim coil control unit 20 in communication with data processingsystem 105. Shim coil control unit 20 may be used for controlling theoperation of shim coils 10.

Conventionally, MRI systems have three basic linear gradient coils 130which generate the x, y, and z gradient fields. In order to correct forlinear spatial variations in the x, y, and z gradient fields, firstorder shimming is usually accomplished by adjusting the dynamic currentthrough gradient coils 130, so no additional hardware may be required tocompensate for first-order concomitant fields. In that regard, gradientcoils 130 may serve a dual function as gradient coils and as“first-order shim coils” in MRI system 100.

In an alternate application, for example, if the fields generated bygradient coils 130 are not sufficiently linear, the first-order linearshim coils may be physically separate from gradient coils 130.

However, as noted above, higher-order non-linear field terms are oftenpresent. Such higher-order terms includes secondary field terms orsecond order terms, which represent second-order concomitant fields.Unlike first-order spatial variations, second-order concomitant fieldsare not linear, but are rather a square term or a product of two spatialdirections. For example, second order yz and zx concomitant fields havespatial variations that are formed by taking the product of a linearvariation along the z-direction, multiplied by a linear variation alongthe y- or x-direction respectively. The z² concomitant fields havespatial variations along a curve represented by the z² function.“Secondary field terms” and “second-order terms” may be usedinterchangeably depending on context. To compensate, active shimming ofthese second-order concomitant fields often requires an additionalelectromagnet system, or additional shim coils.

In an example implementation, a main magnetic field may be representedas B=Bo+three linear terms+five 2^(nd) order terms+seven 3rd order terms+. . . , or more specifically:

$B = {B_{0} + {G_{x}x} + {G_{y}y} + {G_{z}z} + {\frac{1}{8B_{0}}G_{z}^{2}x^{2}} + {\frac{1}{8B_{0}}G_{z}^{2}y^{2}} + {{\frac{1}{2B_{0}}\left\lbrack {G_{x}^{2} + G_{y}^{2}} \right\rbrack}z^{2}} - {\frac{1}{2B_{0}}G_{y}G_{z}{yz}} - {\frac{1}{2B_{0}}G_{x}G_{z}{xz}} + \ldots}$

Some of the terms may be small or zero. For example, if only a ygradient is on (Gy), then the Gx and Gz terms are probably very small orzero, while other higher terms may be present which are not zero.

In that regard, shim coils 10 of MRI system 100 may also includesecond-order (or higher) shim coils. As shown in FIG. 1, shim coils 10may include an x²+y² shim coil 12. Other second-order shim coils thatmay form part of MRI system 100 include a z² shim coil, a zx shim coil,and an yz shim coil. Each of these shim coils may be present in MRIsystem 100 individually or be present in combination with one or more ofthe other second, or higher, order shim coils to correct for concomitantmagnetic fields.

In alternate applications, rather than a specific electromagnet, orspecific shim coil, the second-order shim coil(s) may instead be an“adaptable shim coil”, or a “matrix coil”. A matrix coil or adaptableshim coil is a matrix of electromagnet units that can be controlledindependently of one another, and may be implemented in a number ofdifferent ways. The matrix coil, thus, would be configurable inreal-time to produce the desired spatial field pattern. Furtherdiscussion of matrix coils can be found in Harris et al., “A NewApproach to Shimming: The Dynamically Controlled Adaptive CurrentNetwork” Magnetic Resonance in Medicine, 71:859-869 (2014); and inLittin et al., “Development and Implementation of an 84-Channel MatrixGradient Coil” Magnetic Resonance in Medicine, 79:1181-1191 (2018), bothof which are incorporated herein by reference.

FIG. 2 illustrates an example wire pattern for x²+y² shim coil 12. Thearrows represent an example current direction through x²+y² shim coil12. The second-order shim coils, including the x²+y² shim coil 12, maybe designed in such a way as to reduce coupling between gradient coils130 and shim coils 10, discussed further below.

FIG. 3 is a graph illustrating the z-component of the magnetic field inthe xz-plane that the wire pattern of FIG. 2 produces. FIG. 4 is a graphillustrating the z-component of the magnetic field in the xy-plane thatthe wire pattern of FIG. 2 produces.

x²+y² shim coil 12 is configured to be driven to generate a firstcompensation magnetic field during imaging according to a firstcompensation term. When the z gradient coil is driven, as noted in theabove equation, the first compensation term may be:

(G_(z)²)/(8 * B 0)

In that regard, the first compensation magnetic field has a similaramplitude, but is opposite in direction, to that of the concomitantmagnetic field with an x²+y² spatial variation.

While one example of the wire pattern for x²+y² shim coil 12 is shown,x²+y² shim coil 12 may have other designs and/or wire patterns togenerate the first compensation term and to help correct the concomitantmagnetic field with the x²+y² spatial variation.

In a similar manner as x²+y² shim coil 12, the z² shim coil is designedto help correct the concomitant magnetic field with a z² spatialvariation, the zx shim coil is designed to help correct the concomitantmagnetic field with a zx spatial variation, and the yz shim coil isdesigned to help correct the concomitant magnetic field with a yzspatial variation.

Referring to FIGS. 5 and 6, there are illustrated example methods 500and 600 for reducing a higher order term of a concomitant field in animaging magnetic field during magnetic resonance imaging.

In some examples, methods 500 and 600 may be at least in part beperformed using MRI system 100 as shown in FIG. 1. Additionally, thefollowing discussion of methods 500 and 600 leads to furtherunderstanding of system 100. However, it is to be understood that system100, and methods 500 and 600, can be varied and need not work exactly asdiscussed herein in conjunction with each other, and that suchvariations are within the scope of the appended claims. As well, methods500 and 600 may be performed independently of each other and/orindependently of system 100. Method 500 is described first.

Optionally, at 502, during imaging, the at least one gradient coil isactivated to generate one or more gradient magnetic field. As discussedabove, field homogeneity may be lacking due to concomitant magneticfields (for example, if the z-gradient is activated, the second-orderx²+y² spatial variation may also be present in the magnetic field). Aswell, if more than one gradient coil is activated, multiple second-orderconcomitant magnetic fields may be generated.

At 504, therefore, a first compensation magnetic field with a similaramplitude but opposite direction as that of a first second-orderconcomitant magnetic field is generated with a first shim coil.

Generating the first compensation magnetic field may include designingthe second order shim coil that generates that second-order compensationmagnetic field. In certain applications, the design and manufacture ofthe first shim coil may optionally be performed ahead of time, prior tothe imaging. For example, to arrive at the x²+y² shim coil, a firstcompensation term with the x²+y² spatial variation may be established at506. The first compensation term may be the magnetic field that is equalin magnitude/amplitude but opposite in direction to that of theconcomitant magnetic field with the x²+y² spatial variation. The firstcompensation term may, thus, be mathematically represented by theequation:

(G_(z)²)/(8 * B 0)

In other words, the first compensation term represents the “target”magnetic field that, when superimposed or merged with the gradientmagnetic field in the z direction, nulls or mitigates the concomitantfield with the x²+y² spatial variation.

As a further option, during the optional design and manufacture of theshim coil, at 508, the first compensation term may be processed with amutual inductance constraint. Application of the mutual inductanceconstraint may help to reduce the sensitivity of mutual inductancebetween the x²+y² shim coil and the z-gradient coil, in other words,decouple the x²+y² shim coil from the z-gradient coil.

For example, the mutual inductance may be included as a constraint or aweighted parameter through use of a mutual inductance vectorrepresenting the mutual inductance of the design surface relative to anarray of current elements representing the wire patterns of a targetcoil. Multiple target coils can be included by multiple weightedparameters or multiple simultaneous constraints. The mutual inductancevector can also be calculated at different small translations (e.g.,1-10 mm) or rotations (e.g., 1-3 degrees) of the design surface andincluded as constraints or weighted parameters to reduce mutualinductance that may occur due to anticipated construction positiontolerances.

In one formulation, the mutual inductance vector, M_(n), represents themutual inductance between the finite element surface and a gradient coil130 or another shim coil wire pattern (e.g., the x²+y² shim coil, suchas the wire pattern shown in FIG. 2). For example, the mutual inductancevector can be calculated by the formula:

$M_{n} \approx {\frac{\mu_{0}}{4\pi\; I_{s}}{\int_{S}{\int_{S^{\prime}}{\frac{{J_{in}(r)} \cdot {J_{s}\left( r^{\prime} \right)}}{{r_{in} - r_{s}^{\prime}}}{dS}^{\prime}{dS}}}}}$

where I_(s) is the current amplitude being driven through the targetcoil current element array, J_(in)(r) is the set of current basisfunctions for the finite element surface, J_(s)(s′) is the currentdensity (wire pattern) of the target coil, and |r_(in)−r′_(s)| is thedistance between the node n and the target coil current density.

While one manner of decoupling the x²+y² shim coil from the z-gradientcoil is described above, other decoupling methods may also oralternately be applied to reduce the mutual inductance between the x²+y²shim coil and the z-gradient coil during imaging.

At 510, a x²+y² shim coil may then be designed and created to producethe magnetic field represented by the first compensation term,optionally as constrained with the mutual inductance vector discussedabove.

To design and create the x²+y² shim coil, a performance functional maybe formed with the compensation term and the mutual inductanceconstraint, among other performance metric requirements, to generate acurrent density pattern for the x²+y² shim coil. The performancefunctional may then be optimized based on the performance metricrequirements to get a desired or target current density pattern. Desiredcoil windings for the x²+y² shim coil may then be obtained from thedesired current density pattern, and the x²+y² shim coil maysubsequently be created with the appropriate coil windings.

The x²+y² shim coil is driven with a waveform at 512 to generate thefirst compensation magnetic field. When the x²+y² shim coil is drivenwith the z gradient coil during imaging, the first compensation magneticfield is superimposed or merged with the gradient magnetic field in thez direction, thus nulling or mitigating the concomitant field with thex²+y² spatial variation.

While generating the first compensation magnetic field at 504 has beendescribed using the x²+y² shim coil as the first shim coil, the othersecond-order corrections may be performed in a similar manner. The firstcompensation magnetic field may instead compensate for a concomitantfield with a z² spatial variation using a z² shim coil, compensate for aconcomitant field with a zx spatial variation using a zx shim coil, orcompensate for a concomitant field with a yz spatial variation using ayz shim coil.

In other applications, rather than designing a specific electromagnet(or a specific shim coil) to generate the desired current densitypattern, the adaptable shim coil, or the matrix coil, may be used in aspecific configuration to produce the desired compensation magneticfield. In this manner, the compensation field can be generated inreal-time. The matrix coil would receive input and generate a fielddynamically according to the input given it.

Method 600 is now described with reference to FIG. 6. At 602, multiplegradient magnetic fields are generated. This may include optionallygenerating a z-gradient magnetic field at 607, as described above. Asunderstood by the skilled person, during medical resonance imaging, thez gradient coil may be driven alone or in combination with the xgradient coil and/or the y gradient coil at 602.

In certain applications, a gradient magnetic field in the x directionmay be optionally generated at 604 and/or a gradient magnetic field inthe y direction may be optionally generated at 606. In other words, thex and y gradient coils may also be driven alone or in combination.

In that regard, multiple second-order field terms or higher orderconcomitant magnetic fields may be present in the imaging magneticfield. Thus, multiple compensation magnetic fields may be generated at608 to mitigate these multiple second-order concomitant fields. In theexample shown in FIG. 6, 609 includes generating the first second-ordercompensation magnetic field with the x²+y² spatial variation when thez-gradient coil is driven.

When the x gradient coil or the y gradient coil is driven, a secondcompensation magnetic field may be optionally generated at 610, forexample with a z² shim coil, according to a second second-ordercompensation term. Similar to the first second-order compensation term,the second compensation magnetic field has a similar amplitude butopposite direction as that of the second-order concomitant magneticfield with the z² spatial variation.

In certain applications, the second second-order compensation term isrepresented by:

(G_(x)² + G_(y)²)/(2 * B 0)

The second second-order compensation term represents the “target”magnetic field that, when superimposed or merged with the gradientmagnetic field in the x or y direction, nulls or mitigates thesecond-order concomitant field with the z² spatial variation.

When the x and z gradient coils are driven at the same time, a thirdcompensation magnetic field may be optionally generated at 612, forexample with a zx shim coil, according to a third second-ordercompensation term. Similar to the first second-order compensation term,the third compensation magnetic field has a similar amplitude butopposite direction as that of the second-order concomitant magneticfield with the zx spatial variation.

In certain applications, the third second-order compensation term isrepresented by:

−G_(x) * G_(z)/(2 * B 0)

The third second-order compensation term represents the “target”magnetic field that, when superimposed or merged with the gradientmagnetic field in the x and z direction, nulls or mitigates thesecond-order concomitant field with the zx spatial variation.

When the y and z gradient coils are driven at the same time, a fourthcompensation magnetic field may be optionally generated at 614, forexample with an yz shim coil, according to a fourth second-ordercompensation term. Similar to the first second-order compensation term,the fourth compensation magnetic field has a similar amplitude butopposite direction as that of the second-order concomitant magneticfield with the yz spatial variation.

In certain applications, the fourth second-order compensation term isrepresented by:

−G_(y) * G_(z)/(2 * B 0)

The fourth second-order compensation term represents the “target”magnetic field that, when superimposed or merged with the gradientmagnetic field in the y and z direction, nulls or mitigates thesecond-order concomitant field with the yz spatial variation.

When the x, y, and z gradient coils are driven at the same time, allfour of the above second-order shim coils may be driven as well in orderto mitigate or null their respective second-order concomitant fields. Inother examples, not all of the second-order shim coils may be driven togenerate the compensation magnetic field(s). It should be understoodthat each second-order shim coil may be independently driven to generateindependent compensation magnetic fields, as appropriate, to compensatefor respective second-order field terms.

FIG. 7 provides an example of the above-discussed compensation effectwhen using a z² shim coil. Axial EPI phantom images are shown without(left) and with (right) higher-order concomitant correction (in thiscase, correction of the z² term) for a slice 5.0 mm (top) and 75.0 mm(bottom) off isocenter respectively. The images on the right arebrighter. For a slice near isocenter (top), the high-order correctiondoes not significantly affect the signal of the phantom. This isindicated by the mean and standard deviation of the signal. Withoutcorrection (top left), the mean and standard deviation of the signal is4796.3 and 109.3, respectively. With correction (top right), the meanand standard deviation of the signal is 4657.7 and 95.2, respectively.

However, for a slice further from isocenter (bottom), the correctionincreases the signal of the phantom by approximately 25%. Withoutcorrection (bottom left), the mean and standard deviation of the signalis 2545.2 and 126.2, respectively. With correction (bottom right), themean and standard deviation of the signal is 3386.1 and 142.3,respectively. The higher number of the mean for the corrected caseillustrates how the correction helps to recover some lost signal due todropout from the higher order concomitant magnetic fields. As notedabove, for an axial EPI image with readout on either the x- ory-gradient axes, the high-order concomitant correction is applied usingthe z² shim coil.

As such, when a x²+y², zx, yz, and/or z² concomitant magnetic field ispresent, it may be compensated for in real-time by running therespective x²+y², zx, yz, and/or z² shim coils such that the two fieldeffects (one due to the concomitant field and one due to the shim coil)cancel each other out.

Generally, there are four second-order concomitant magnetic fields (xy,yz, zx, x²+y², and z²), which are generated by a Taylor expansion of themain magnetic field. In a typical second-order active shimming system,there are four second-order electromagnets (xy, yz, zx, x²−y², and z²),which are based on a spherical harmonic expansion of the magnetic field.The mismatch in spatial patterns between the two expansions, that isx²+y² and x²−y² for the concomitant field term and shim field termrespectively, necessitates an additional, novel, correctionelectromagnet for full second-order compensation, i.e. an electromagnetthat produces an x²+y² spatial pattern. This helps to illustrate thenovelty of using the second-order shim coils for concomitant fieldcorrection as presently described.

This compensation may be done in real-time, similar to eddy currentcompensation. This is possible because the amplitude of the concomitantmagnetic field terms are well-defined with respect to the gradient coilamplitudes and the main magnetic field.

In some implementations, an advantage of the presently disclosed methodand system may be that it is not specific to a particular imageorientation. The presently disclosed system and method may provide thedesired reduction of concomitant field regardless of the orientation ofthe image. As well, the presently disclosed solution may require littleor no modifications to the post-processing reconstruction method, andmay not require the images to be de-rated to achieve artefact freeimages. This may help to enable faster imaging.

It will be appreciated that the above magnetic field compensationmethods and systems may be implemented alone or in combination withother compensation methods and systems, including passive shimming,depending on the type and severity of the field instability.

While the magnetic field compensation described relates to second-orderconcomitant magnetic fields, the above methods and systems may also beapplied to third order, or higher, concomitant magnetic fields.

The effect of the concomitant fields tends to get smaller as the spatialterms get higher in order. However, correction of third order or higherorder concomitant magnetic fields may be relevant in applications wherethe main magnetic field strength is lower.

While some embodiments or aspects of the present disclosure may beimplemented in fully functioning computers and computer systems, otherembodiments or aspects may be capable of being distributed as acomputing product in a variety of forms and may be capable of beingapplied regardless of the particular type of machine or computerreadable media used to actually effect the distribution.

At least some aspects disclosed may be embodied, at least in part, insoftware. That is, some disclosed techniques and methods may be carriedout in a computer system or other data processing system in response toits processor, such as a microprocessor, executing sequences ofinstructions contained in a memory, such as read-only memory (ROM),volatile random access memory (RAM), non-volatile memory, cache or aremote storage device.

A computer readable storage medium may be used to store software anddata which when executed by a data processing system causes the systemto perform various methods or techniques of the present disclosure. Theexecutable software and data may be stored in various places includingfor example ROM, volatile RAM, non-volatile memory and/or cache.Portions of this software and/or data may be stored in any one of thesestorage devices.

Examples of computer-readable storage media may include, but are notlimited to, recordable and non-recordable type media such as volatileand non-volatile memory devices, ROM, RAM, flash memory devices, floppyand other removable disks, magnetic disk storage media, optical storagemedia (e.g., compact discs (CDs), digital versatile disks (DVDs), etc.),among others. The instructions can be embodied in digital and analogcommunication links for electrical, optical, acoustical or other formsof propagated signals, such as carrier waves, infrared signals, digitalsignals, and the like. The storage medium may be the internet cloud, ora computer readable storage medium such as a disc.

Furthermore, at least some of the methods described herein may becapable of being distributed in a computer program product comprising acomputer readable medium that bears computer usable instructions forexecution by one or more processors, to perform aspects of the methodsdescribed. The medium may be provided in various forms such as, but notlimited to, one or more diskettes, compact disks, tapes, chips, USBkeys, external hard drives, wire-line transmissions, satellitetransmissions, internet transmissions or downloads, magnetic andelectronic storage media, digital and analog signals, and the like. Thecomputer useable instructions may also be in various forms, includingcompiled and non-compiled code.

At least some of the elements of the systems described herein may beimplemented by software, or a combination of software and hardware.Elements of the system that are implemented via software may be writtenin a high-level procedural language such as object oriented programmingor a scripting language. Accordingly, the program code may be written inC, C++, J++, or any other suitable programming language and may comprisemodules or classes, as is known to those skilled in object orientedprogramming. At least some of the elements of the system that areimplemented via software and hardware may be written in assemblylanguage, machine language or firmware as needed.

In either case, the program code can be stored on storage media or on acomputer readable medium that is readable by a general or specialpurpose programmable computing device having a processor, an operatingsystem and the associated hardware and software that is necessary toimplement the functionality of at least one of the embodiments describedherein. The program code, when read by the computing device, configuresthe computing device to operate in a new, specific and predefined mannerin order to perform at least one of the methods described herein.

While the teachings described herein are in conjunction with variousembodiments for illustrative purposes, it is not intended that theteachings be limited to such embodiments. On the contrary, the teachingsdescribed and illustrated herein encompass various alternatives,modifications, and equivalents, without departing from the describedembodiments, the general scope of which is defined in the appendedclaims. Except to the extent necessary or inherent in the processesthemselves, no particular order to steps or stages of methods orprocesses described in this disclosure is intended or implied. In manycases the order of process steps may be varied without changing thepurpose, effect, or import of the methods described.

1. A magnetic resonance imaging (MRI) system comprising: anelectromagnet system for reducing a higher order term of a concomitantfield in an imaging magnetic field during magnetic resonance imaging,the electromagnet system having: a first shim coil configured to bedriven to generate a first compensation magnetic field during imagingaccording to a first second-order compensation term, the firstcompensation magnetic field having a similar amplitude but oppositedirection as that of a first second-order concomitant magnetic field;and a second shim coil configured to be driven to generate an additionalcompensation magnetic field during imaging according to an additionalsecond-order compensation term, the additional compensation magneticfield having a similar amplitude but opposite direction as that of anadditional second-order concomitant magnetic field.
 2. The MRI system ofclaim 1, wherein the first shim coil is an x²+y² shim coil and the firstsecond-order concomitant magnetic field has an x²+y² spatial variation.3. The MRI system of claim 1, wherein the first shim coil is one of: az² shim coil and the first second-order concomitant magnetic field has az² spatial variation, a zx shim coil and the first second-orderconcomitant magnetic field has a zx spatial variation, and a yz shimcoil and the first second-order concomitant magnetic field has a yzspatial variation.
 4. The MRI system of claim 2, wherein the second shimcoil comprises a z² shim coil, a zx shim coil, or a yz shim coil, the z²shim coil configured to be driven to generate a second compensationmagnetic field during imaging according to a second second-ordercompensation term, the second compensation magnetic field having asimilar amplitude but opposite direction as that of a secondsecond-order concomitant magnetic field with a z² spatial variation, thesecond compensation magnetic field being the additional compensationmagnetic field, the second second-order compensation term being theadditional second-order compensation term, and the second second-orderconcomitant magnetic field being the additional second-order concomitantmagnetic field, the zx shim coil configured to be driven to generate athird compensation magnetic field during imaging according to a thirdsecond-order compensation term, the third compensation magnetic fieldhaving a similar amplitude but opposite direction as that of a thirdsecond-order concomitant magnetic field with a zx spatial variation, thethird compensation magnetic field being the additional compensationmagnetic field, the third second-order compensation term being theadditional second-order compensation term, and the third second-orderconcomitant magnetic field being the additional second-order concomitantmagnetic field, and the yz shim coil configured to be driven to generatea fourth compensation magnetic field during imaging according to afourth second-order compensation term, the fourth compensation magneticfield having a similar amplitude but opposite direction as that of afourth second-order concomitant magnetic field with a yz spatialvariation, the fourth compensation magnetic field being the additionalcompensation magnetic field, the fourth second-order compensation termbeing the additional second-order compensation term, and the fourthsecond-order concomitant magnetic field being the additionalsecond-order concomitant magnetic field.
 5. The MRI system of claim 4,further comprising a third shim coil and a fourth shim coil, the second,third, and fourth shim coils comprising the z² shim coil, the zx shimcoil, and the yz shim coil, respectively.
 6. The MRI system of claim 4,wherein the second second-order compensation term is (Gx²+G_(y)²)/(2*B0), the third second-order compensation term is−G_(x)*G_(z)/(2*B0), and the fourth second-order compensation term is−G_(y)*G_(z)/(2*B0).
 7. The MRI system of claim 1, wherein the firstshim coil is a matrix coil.
 8. A method for reducing a higher order termof a concomitant field in an imaging magnetic field during magneticresonance imaging, the method comprising: generating a firstcompensation magnetic field with a first shim coil during imagingaccording to a first second-order compensation term, the firstcompensation magnetic field having a similar amplitude but oppositedirection as that of a first second-order concomitant magnetic field;and generating an additional compensation magnetic field with a secondshim coil during imaging according to an additional second-ordercompensation term, the additional compensation magnetic field having asimilar amplitude but opposite direction as that of an additionalsecond-order concomitant magnetic field.
 9. The method of claim 8,wherein the first shim coil is an x²+y² shim coil and the firstsecond-order concomitant magnetic field has an x²+y² spatial variation.10. The method of claim 8, wherein the first shim coil is one of: a z²shim coil and the first second-order concomitant magnetic field has a z²spatial variation, a zx shim coil and the first second-order concomitantmagnetic field has a zx spatial variation, and a yz shim coil and thefirst second-order concomitant magnetic field has a yz spatialvariation.
 11. The method of claim 9, wherein generating the firstcompensation magnetic field comprises: designing and creating the x²+y²shim coil to produce the compensation magnetic field; and driving thex²+y² shim coil during magnetic resonance imaging.
 12. The method ofclaim 9, wherein the additional compensation magnetic field comprises asecond, a third, or a fourth compensation magnetic field, the secondcompensation magnetic field being generated with a z² shim coilaccording to a second second-order compensation term, the secondcompensation magnetic field having a similar amplitude but oppositedirection as that of a second second-order concomitant magnetic fieldwith a z² spatial variation, the z² shim coil being the second shimcoil, the second second-order compensation term being the additionalsecond-order compensation term, and the second second-order concomitantmagnetic field being the additional second-order concomitant magneticfield, the third compensation magnetic field being generated with a zxshim coil according to a third second-order compensation term, the thirdcompensation magnetic field having a similar amplitude but oppositedirection as that of a third second-order concomitant magnetic fieldwith a zx spatial variation, the zx shim coil being the second shimcoil, the third second-order compensation term being the additionalsecond-order compensation term, and the third second-order concomitantmagnetic field being the additional second-order concomitant magneticfield, and the fourth compensation magnetic field being generated with ayz shim coil according to a fourth second-order compensation term, thefourth compensation magnetic field having a similar amplitude butopposite direction as that of a fourth second-order concomitant magneticfield with a yz spatial variation, the yz shim coil being the secondshim coil, the fourth second-order compensation term being theadditional second-order compensation term, and the fourth second-orderconcomitant magnetic field being the additional second-order concomitantmagnetic field.
 13. The method of claim 12, wherein the secondsecond-order compensation term is (G_(x) ²+G_(y) ²)/(2*B0), the thirdsecond-order compensation term is −G_(x)*G_(z)/(2*B0), and the fourthsecond-order compensation term is −G_(y)*G_(z)/(2*B0).
 14. The method ofclaim 12, further comprising generating two further additionalcompensation magnetic fields, the additional compensation magnetic fieldand the two further additional compensation magnetic fields comprisingthe second, third, and fourth compensation magnetic fields,respectively.
 15. An electromagnet set for reducing a higher order termof a concomitant field in an imaging magnetic field during magneticresonance imaging, the electromagnet set comprising: a firstelectromagnet configured to be driven to generate a first compensationmagnetic field during imaging according to a first second-ordercompensation term, the first compensation magnetic field having asimilar amplitude but opposite direction as that of a first second-orderconcomitant magnetic field a second electromagnet configured to bedriven to generate an additional compensation magnetic field duringimaging according to an additional second-order compensation term, theadditional compensation magnetic field having a similar amplitude butopposite direction as that of an additional second-order concomitantmagnetic field.
 16. The electromagnet set of claim 15, wherein the firstelectromagnet is an x²+y² shim coil for correcting the firstsecond-order concomitant magnetic field with an x²+y² spatial variation.17. The electromagnet set of claim 15, wherein the first electromagnetis one of: a z² shim coil for correcting the first second-orderconcomitant magnetic field with a z² spatial variation, a zx shim coilfor correcting the first second-order concomitant magnetic field with azx spatial variation, and a yz shim coil for correcting the firstsecond-order concomitant magnetic field with a yz spatial variation. 18.The electromagnet set of claim 16, wherein second electromagnet is a z²shim coil, a zx shim coil, or a yz shim coil, the z² shim coilconfigured to be driven to generate a second compensation magnetic fieldduring imaging according to a second second-order compensation term, thesecond compensation magnetic field having a similar amplitude butopposite direction as that of a second second-order concomitant magneticfield with a z² spatial variation, the second compensation magneticfield being the additional compensation magnetic field, the secondsecond-order compensation term being the additional second-ordercompensation term, and the second second-order concomitant magneticfield being the additional second-order concomitant magnetic field, thezx shim coil configured to be driven to generate a third compensationmagnetic field during imaging according to a third second-ordercompensation term, the third compensation magnetic field having asimilar amplitude but opposite direction as that of a third second-orderconcomitant magnetic field with a zx spatial variation, the thirdcompensation magnetic field being the additional compensation magneticfield, the third second-order compensation term being the additionalsecond-order compensation term, and the third second-order concomitantmagnetic field being the additional second-order concomitant magneticfield, and the yz shim coil configured to be driven to generate a fourthcompensation magnetic field during imaging according to a fourthsecond-order compensation term, the fourth compensation magnetic fieldhaving a similar amplitude but opposite direction as that of a fourthsecond-order concomitant magnetic field with a yz spatial variation, thefourth compensation magnetic field being the additional compensationmagnetic field, the fourth second-order compensation term being theadditional second-order compensation term, and the fourth second-orderconcomitant magnetic field being the additional second-order concomitantmagnetic field.
 19. The electromagnet set of claim 18, furthercomprising a third electromagnet and a fourth electromagnet, the second,third, and fourth electromagnets comprising the z² shim coil, the zxshim coil, and the yz shim coil, respectively.